WASHINGTON — The Senate is moving forward on a compromise bill to help veterans avoid long waits to see a doctor and make it easier to fire administrators who falsify records to cover up long wait times.

Hopes for a vote as soon as Thursday have dimmed, but senators said they would press ahead on a measure to address an uproar over veterans’ health care following allegations that veterans have died while waiting to see a Veterans Affairs doctor.

Senators had wanted to pass the bill before Friday’s 70th anniversary of the Allied invasion of Europe in World War II. Up to a dozen senators were expected to attend the D-Day ceremonies in France.

Sen. Bernie Sanders, I-Vt., chairman of the Senate Veterans Affairs Committee, had said Wednesday he was “cautiously optimistic” that a vote could be held Thursday.

Sanders and Republican Sen. John McCain of Arizona were leading negotiations on the bill, holding two closed-door meetings Wednesday to iron out details.

But a spokesman for Sanders said Wednesday night that talks would continue Thursday, making an immediate vote unlikely. Senators fly to France on Thursday evening.

“Chairman Sanders held productive discussions today with Sen. McCain and others about how to provide high-quality health care to veterans in a timely manner,” Sanders spokesman Michael Briggs said.

Sanders “hopes to reach an agreement to take before the full Senate as soon as possible,” Briggs added.

Talks on the bill were resuming as the Obama administration’s new veterans affairs chief visits the Phoenix hospital at the center of allegations that veterans died while waiting to see a VA doctor. Acting VA Secretary Sloan Gibson was scheduled to tour the Phoenix hospital and speak with officials there. A former clinic director has said up to 40 veterans may have died while awaiting treatment in Phoenix.

Sanders, a self-described socialist, acknowledged that he and McCain, the 2008 Republican nominee for president, make an unlikely pair, but he was upbeat about the prospects of quickly reaching a deal.

McCain was less optimistic about a bill being passed this week. “I am not predicting anything,” he told reporters Wednesday.

The main stumbling block appeared to be over when and under what circumstances veterans could turn to doctors and other providers outside the 1,700-facility VA system for what is largely free care for them.

The two lead negotiators couldn’t agree on how to define it. Sanders said the primary issue was waiting times, while McCain said it was giving veterans a choice beyond the VA for receiving care.

A bill sponsored by Sanders would allow veterans who can’t get timely appointments with VA doctors to go to community health centers, military hospitals or private doctors.

McCain would rather let veterans who can’t get a VA appointment within 30 days or who live more than 40 miles from a VA hospital or clinic go to any doctor who participates in Medicare or the military’s TRICARE program. He complained that Sanders’ approach “has the VA bureaucrat decide whether that veteran should get the health care of their choice.”

An interim report by the VA’s inspector general said veterans in Phoenix wait an average of 115 days for a first appointment — five times longer than the 24-day average the hospital had reported. The inspector general said at least 42 VA facilities nationwide were under investigation, including the Phoenix VA hospital, where a former clinic director said as many as 40 veterans may have died while awaiting treatment.

Rep. Jeff Miller, R-Fla., chairman of the House VA panel, said Sanders’ approach did not do enough to hold senior officials at the VA accountable for falsified waiting lists and other problems. The House last month passed a bill by Miller that would allow the VA to immediately fire as many as 450 regional executives and hospital administrators for poor performance.

Those officials are largely responsible for reports of falsified records and secret waiting lists, since many received bonuses based on seeming adherence to VA guidelines on patient wait times, Miller said.

“Some VA health officials are so driven in their quest for performance bonuses, promotions and power that they are willing to lie, cheat and put the health of the veterans they were hired to serve at risk,” he said. “These are not people who deserve a second chance. They deserve a swift exit from federal employment and possibly an entrance to federal prison.”